The Radbaz (Rav David Ben Zimra, Egypt, 1479-1573), in discussing the obligation to respect one’s parents, writes that if a person is called for Shelishi – the third Aliya to the Torah in the synagogue – then his son should not later be called for Shishi – the sixth Aliya. As receiving the sixth Aliya is regarded as a more prestigious honor than receiving the third, it would be inappropriate and an infringement upon the father’s honor if he receives the third Aliya and his son receives the sixth Aliya. The Mesader (person who calls people to the Torah) must therefore ensure not to call somebody for Shishi if his father had received an earlier Aliya.
The Radbaz goes so far as to rule that if the son is called for Shishi in such a case, even if he is called by name, he should refuse the Aliya. Although it is generally improper to refuse an Aliya after being called by name, in such a case, the son must refuse the Aliya in order not to disrespect his father.
Summary: A person should not be given the sixth Aliya in the synagogue if his father had received an earlier Aliya, as the sixth Aliya is considered the most prominent Aliya, and this would thus be disrespectful to the father.